cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A182965 E.g.f.: A(x) = Product_{n>=1} (1 + 2*x^n/n)^n.

Original entry on oeis.org

1, 2, 4, 36, 168, 1440, 13920, 134400, 1619520, 20549760, 294631680, 4449096960, 74429752320, 1312794362880, 24870628823040, 501316411115520, 10661299747338240, 239672059847700480, 5664762159214878720
Offset: 0

Views

Author

Paul D. Hanna, Dec 19 2010

Keywords

Examples

			E.g.f.: A(x) = 1 + 2*x + 4*x^2/2! + 36*x^3/3! + 168*x^4/4! +...
A(x) = (1+2x)*(1+2x^2/2)^2*(1+2x^3/3)^3*(1+2x^4/4)^4*(1+2x^5/5)^5*...
		

Crossrefs

Programs

  • Mathematica
    nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 07 2020 *)
  • PARI
    {a(n,k=2)=n!*polcoeff(prod(m=1,n,(1+k*x^m/m+x*O(x^n))^m),n)}

A182966 E.g.f.: A(x) = Product_{n>=1} (1 + 3*x^n/n)^n.

Original entry on oeis.org

1, 3, 6, 72, 342, 3330, 36720, 366660, 4974480, 67178160, 1043189280, 16836906240, 303306806880, 5705780240160, 114832957599360, 2475901844095680, 55754442891987840, 1331875774475326080, 33292197644365820160
Offset: 0

Views

Author

Paul D. Hanna, Dec 19 2010

Keywords

Examples

			E.g.f.: A(x) = 1 + 3*x + 6*x^2/2! + 72*x^3/3! + 342*x^4/4! +...
A(x) = (1+3x)*(1+3x^2/2)^2*(1+3x^3/3)^3*(1+3x^4/4)^4*(1+3x^5/5)^5*...
		

Crossrefs

Programs

  • Mathematica
    nmax = 20; CoefficientList[Series[Product[(1 + 3*x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 07 2020 *)
  • PARI
    {a(n,k=3)=n!*polcoeff(prod(m=1,n,(1+k*x^m/m+x*O(x^n))^m),n)}
Showing 1-2 of 2 results.